An oxidative hair dye composed of the first part containing an alkali agent, a precursor, and a coupler and the second part containing hydrogen peroxide is preferable because gray hair can be more evenly dyed and in that a hair color is greatly changed, as compared to other hair dyes, and thus has been widely used in general. This is derived from characteristics that in an oxidative hair dyes, alkaline hydrogen peroxide decomposes melanin inside hair and a color of the hair can be thus bleached to be brightened. Particularly, in recent years, it has become preferred that black and white hair is dyed without unevenness with more bright colors and with bright and vivid color tone, and there has been a tendency that higher bleaching ability is required.
In order to obtain higher bleaching ability, it is considered that an alkali agent or an oxidizing agent is contained in a large amount, but there is a possibility of causing problems such that, depending on its amount, strong pungent odor is accompanied, hair damage proceeds, and irritation is given to scalp.
Accordingly, a method of containing a specific triazacyclononane compound in hair dyes (Patent Document 1) and a method of containing a specific cyclic amine compound in a hair dye (Patent Document 2) have been proposed. However, these methods are insufficient for obtaining high bleaching ability with less pungent odor and less hair damage.    [Patent Document 1] JP-A-2002-255763    [Patent Document 2] WO Publication No. 2003/051322